Abstract

The term “hybrid system” refers to a continuous time dynamical system that undergoes Markovian perturbations at discrete time intervals. In this paper, we find that under the right formulation, a hybrid system can be treated as a dynamical system on a compact space. This allows us to study its limit sets. We examine the Morse decompositions of hybrid systems, find a sufficient condition for the existence of a non-trivial Morse decomposition, and study the Morse sets of such a decomposition. Finally, we consider the case in which the Markovian perturbations are small, showing that trajectories in a hybrid system with small perturbations behave similarly to those of the unperturbed dynamical system.

K. Ayers was supported by DMS 0502354. X. Garcia was supported by DMS 0750986 and DMS 0502354. J. Kunze was supported by DMS 0750986. T. Rudelius was supported by DMS 0750986. A. Sanchez was supported by DMS 0750986 and DMS 0502354. S. Shao was supported by Iowa State University. E. Speranza was supported by DMS 0750986.